Enumerating pseudo-triangulations

Pseudo-Triangulation.
Pseudo-triangle is a simple polygon with exactly three convex
vertices.
Pseudo-triangulation of n points is a partition
of their convex hull into interior disjoint pseudo-triangles whose
vertices are given points.
Minimum pseudo-triangulation of S is a
pseudo-triangulation with the least number of edges among all
pseudo-triangulations of S.

Fig. 1. Pseudo-triangle.

Fig. 2. Minimum pseudo-triangulation of 11 points.

The basic operation on pseudo-triangulations is a flip.

Fig. 3. (a) Flip of traingles, (b) flip of pseudo-triangles.

Graph of pseudo-triangulations.
We study the graph G whose vertices represent the
pointed (or minimum) pseudo-triangulations of given points and whose
edges represent flips.
The graph G is connected.
We construct a spanning tree of G, see Fig. 4 for an example.
Based on the spanning tree we show that the pseudo-triangulations can
be enumerated in O(logn) time per
pseudo-triangulation.